We employ a well-known class of designs to give a complete solution to the problem of determining the spectrum of uniform semiframes with block size two. As a corollary we prove that the complete graph \(K_{gu}\), admits a one-factorization with an orthogonal set of \(u\) disjoint sub-one-factorizations of \(K_g\) if and only if \(g\) is even and \(u\geq3\).